Thank You for Smoking
I don’t think they’re based on stage plays, but I liked the Whit Stillman films Metropolitan and Barcelona (and, to a lesser extent, The Last Days of Disco). If you like dialogue-heavy movies, you might like them.
The Man From Earth is nothing but dialogue and it’s brilliant.
Kiss Kiss Bang Bang is film noir in the early 21st century and is not Sidney Lumet- or David Mamet- involved.
And in the category the OP spoke of, “these ‘smartest guys in the room showing up everyone’ kind of movies”, let’s not forget Ace Ventura: Pet Detective; cite. 
Margin Call is a much better movie than The Big Short IMHO and all of JC Chandor’s other movies are worth watching.
Except if you want dialogue-heavy movies, I don’t think you’d like All Is Lost (one of JC Chandor’s movies).
What are you talking about? The dialogue between Robert Redford’s left eyebrow and Robert Redford’s right eyebrow had me riveted through the entire movie.
The Clooney/Pitt/Damon Oceans 11
For something different, Gilmore Girls has really smart snappy dialog, though it gets boring after a season.
Also different, the Miss Fisher Murder Mysteries.
In fact, all of the Coen Brothers’ movies have a certain intelligence to them (that may or may not be along the lines of the kind of thing the OP is looking for).
I reckon “Lucky number Slevin” would be right up your alley. Can’t really tell more without spoiling. Can I get a witness?
Aye, it’s a decent flick. Also the only time I could stand Lucy Liu (she’s terrific in this).
How about Absence Of Malice or The Verdict?
There is a Bruce Willis/Richard Gere remake of this which, while it isn’t terrible, is best avoided. I agree the original was completely brilliant, as is the book by Frederick Forsythe if you’re interested.